Question 2 A recent census of cmployees at a large automotive company showcd tha

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Question 2 A recent census of cmployees at a large automotive company showcd that 30% of the assembly linc workers w ere extremely bored with their job. The management of the company arranged for a consing firm to come and offer a program to reduce on-the -job boredom. After two months of the program, a random sample of 13 workers was selected to help evaluate its impact. a) What probability distribution describes the number of workers being bored with their jobs? Name Parameters b) Find the mean and standard deviation of the number of workers being bored with their jobs? Mean: Standard deviation: c) If the program was not effective, what is the probability that exactly 6 workers in the sample would report being bored with their job? (First translate words into symbols - you have to do this for a quiz or exam) d) If the program was not effective, what is the probability that more than 6 workers in the sample would report bcing bored with thcir job? e) If the program was not effective, what is the probability that at most 6 workers in the sample would report being bored with their job? If the program would report being bored with their job? was not effective, what is the probability that more than 5 but at most 9 workers in the sample

Explanation / Answer

(a) Number of workers being bored with their jobs follows Binomial (13,0.3)

Name : Binomial disctribution

Parameters : n = 13 , p (probability of workers bored with theri job), p = 0.3

(b) Mean : np = 13*0.3 = 3.9

Standard deviation : (np(1-p))0.5 = (13*0.3*0.7)0.5 = 1.6523

(c) Let x be the number of people bored with thier jobs

To find : P(x=6) = nCx (p)x (1-p)n-x

= 13C6 (0.3)6 (0.7)7

=0.1030

(d) P(x>6) = P(x=7)+P(x=8)+P(x=9)+P(x=10)+P(x=11)+P(x=12)+P(x=13)

= 13C7 (0.3)7 (0.7)6 +......................+ 13C13 (0.3)13 (0.7)0

= 0.0442 + 0.0142 + .......+ 0.0000

=0.0624

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